Ocean dynamics can affect many aspects of operations near the coastline. In military operations, for example, operation of small craft and Unmanned Undersea Vehicles can be significantly affected by the dynamics of the ocean or other bodies of water near the coastline. In conventional civilian applications, such coastal dynamics can also play an important part in activities such as planning and operation of recreation facilities, fishing (both recreational and commercial), and coastal engineering projects.
Among the geological features that affect ocean dynamics near the coastline are the bottom type (friction features) and bathymetry of the ocean floor. The friction features, which are on the order of 100 km2 in area, represent variations in bottom characteristics such as bed forms and sediment type. The spatial scale of sediment heterogeneity varies, but mud banks can be as much as 1800 km2 in extent whereas individual ripples are much smaller. See E. J. Anthony, A. Gardel, F. Dolique, and D. Guiral (2002), “Short-term changes in the plan shape of a sandy beach in response to sheltering by a nearshore mud bank, Cayenne, French Guiana,” Earth Surf. Processes Landforms, 27, 857-866. Bathymetric features include depressions such as drowned river valleys and elevated areas such as shoals and sand ridges. See R. A. McBride and T. F. Moslow (1991), “Origin, evolution, and distribution of shoreface sand ridges, Atlantic inner shelf, U.S.A.,” Mar. Geol., 97, 57-85.
Although it is not possible to completely observe the global ocean, remote sensing has made it easier to measure sea surface properties over large regions. Satellites and coastal radar have provided dense data sets that can be used to analyze wave motion and other aspects of ocean and coastal dynamics. See, for example, Haus, B. K. (2007), “Surface current effects on the fetch-limited growth of wave energy,” J. Geophys. Res., 112, C03003, doi:10.1029/2006JC003924. Synthetic Aperture Radar (SAR) data can be processed to retrieve wave heights but can have high error rates, in some cases as much as 29%. See C. Mastenbroek and C. F. de Valk (2000), “A semiparametric algorithm to retrieve ocean wave spectra from synthetic aperture radar,” J. Geophys. Res., 105, 3497-3516. Shore-based radar systems such as those described in by Gurgel et al. could also be useful for providing wave measurements. K. W. Gurgel, G. Antonischki, H. H. Essen, and T. Schlick (1999), “Wellen Radar (WERA): A new ground-wave HF radar for ocean remote sensing,” Coastal Eng., 37, 219-234. These approaches have problems but their continued development suggests that dense wave height observations with errors less than 10% are not an unreasonable expectation in the future.
However, observation of the seafloor is more problematic. Key aspects of the seafloor that can be very important to determine are the shape, size, and makeup of bottom friction fields. Although bottom friction is not critical to understanding the dynamics of ocean currents in deep water, it can be an important factor affecting both currents and waves in the shallow water over the continental shelf. Moreover, the ability to isolate bottom friction errors from water depth errors is crucial to evaluate bottom sediment type using wave observations.
When the water depth is less than the deep-water wavelength of wind-generated surface waves, bottom friction can produce observable changes in the surface wave properties, for example, by dissipating wave energy as waves propagate over the fields. Research on wave dynamics affected by friction fields has been carried out by many researchers. See, for example, A. Sheremet and G. W. Stone (2003), “Observations of nearshore wave dissipation over muddy sea beds,” J. Geophys. Res., 108(C11), 3357; F. Ardhuin, W. C. O'Reilly, T. H. C. Herbers, and P. F. Jessen (2003), “Swell transformation across the continental shelf. Part I: Attenuation and directional broadening,” J. Phys. Oceanogr., 33, 1921-1939; and J. M. Kaihatu and A. Sheremet (2004), “Dissipation of wave energy by cohesive sediments,” in Coastal Engineering 2004, edited by J. M. Smith, pp. 498-507.
The changes in ocean surface properties due to bottom friction fields can be observed remotely, as can other ocean surface properties like wave energy spectra and temperature. However, when only surface properties are available, it may be difficult to determine the causes of the observed changes. Consequently, ocean scientists have begun to utilize inverse techniques, which can improve our knowledge of physical processes from observations.
One kind of inverse method is data assimilation, which combines model physics with observations to provide a better picture of the ocean than can be deduced from either form of analysis alone. See D. L. T. Anderson, J. Sheinbaum, and K. Haines (1996), “Data assimilation in ocean models,” Rep. Prog. Phys., 59, 1209-1266.
Data assimilation techniques can take many forms, and range from nudging numerical models with observations to direct assimilation of observations using variational approaches. See F. X. Le Dimet and O. Talagrand (1986), “Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects,” Tellus, Ser. A, 38, 97-110; A. F. Bennett (1992), Inverse Methods in Physical Oceanography, 346 pp.; and L. Bertino, G. Evensen, and H. Wackernagel (2003), “Sequential data assimilation techniques in oceanography,” Int. Stat. Rev., 71, 223-241.
In the oceanographic field, data assimilation has been used to improve numerical wave forecasts by nudging wave models with observations from wave buoys and remote sensing. See W. C. O'Reilly and R. T. Guza (1998), “Assimilating coastal wave observations in regional swell predictions. Part I: Inverse methods,” J. Phys. Oceanogr., 28, 679-691; L. H. Holthuijsen, N. Booij, M. vanEndt, S. Caires, and C. G. Soares (1997), “Assimilation of buoy and satellite data in wave forecasts with integral control variables,” J. Mar. Syst., 13, 21-31; J. R. Bidlot and M. W. Holt (1999), “Numerical wave modeling at operational weather centres,” Coastal Eng., 37, 409-429; and D. J. M. Greenslade (2001), “The assimilation of ERS-2 significant wave height data in the Australian region,” J. Mar. Syst., 28, 141-160.
In addition to its use in improving wave forecasting, data assimilation has also proven useful in estimating water depth using inverse techniques. See R. A, Dalrymple, A. B. Kennedy, J. T. Kirby, and Q. Chen (1998), “Determining bathymetry from remotely sensed images,” Coastal Engineering 1998, edited by B. Edge, pp. 2395-2408; S. T. Grilli (1998), “Depth inversion in shallow water based on nonlinear properties of shoaling periodic waves,” J. Coastal Eng., 35, 185-209; and C. Wackerman, D. Lyzenga, E. Ericson, and D. Walker (1998), “Estimating near-shore bathymetry using SAR,” in Proceedings of the 1998 International Geoscience and Remote Sensing Symposium: Sensing and Managing the Environment, edited by T. I. Stein, pp. 1668-1670, Inst. Of Electr. and Electr. Eng., New York. Iterative approaches are necessary for depth inversions based on numerical wave modeling. See A. B. Kennedy, R. A. Dalrymple, J. T. Kirby, and Q. Chen (2000), “Determination of inverse depths using direct Boussinesq modeling,” J. Waterw. Port Coastal Ocean Eng., 126, 206-214. It also may be possible to perform joint inversions for bottom friction and bathymetry, see K. T. Holland (2001), “Application of the linear dispersion relation with respect to depth inversion and remotely sensed imagery,” IEEE Trans. Geosci. Remote Sens., 39, 2060-2072.
Data assimilation requires that some assumptions be made with respect to the relationships between the data and model parameters being investigated. Numerical wave models that include physical phenomena such as shoaling, dissipation, bottom friction and refraction can permit a comprehensive examination of complex processes.
However, in order to use a numerical wave model in an inverse solution, it is necessary to first identify the key model parameters. Key model parameters are those upon which all other parameters have a high dependency. They can be identified by sensitivity analyses using a numerical model. See N. Z. Sun, M. Elimelech, and J. N. Ryan (2001), “Sensitivity analysis and parameter identifiability for colloid transport in geochemically heterogeneous porous media,” Water Resour. Res., 37, 209-222; and R. Weisse and F. Feser (2003), “Evaluation of a method to reduce uncertainty in wind hindcasts performed with regional atmospheric models,” Coastal Eng., 48, 211-225. However, if a complex model is used, it is important to test for consistency in the selection of key parameters. See M. B. Beck (1987), “Water-quality modeling: A review of the analysis of uncertainty,” Water Resour. Res., 23, 1393-1442; and F. Feddersen, E. L. Gallagher, R. T. Guza, and S. Elgar (2003), “The drag coefficient, bottom roughness, and wave-breaking in the nearshore,” Coastal Eng., 48, 189-195.
Numerical wave models have previously been used in an iterative procedure to study the bottom friction field. See, for example, A. B. Kennedy, R. A. Dalrymple, J. T. Kirby, and Q. Chen (2000), “Determination of inverse depths using direct Boussinesq modeling,” J. Waterw. Port Coastal Ocean Eng., 126, 206-214; Narayanan, C., V. N. R. Rao, and J. M. Kaihatu (2004), “Model parameterization and experimental design issues in nearshore bathymetry inversion,” J. Geophys. Res., 109, C08006, doi:10.1029/2002JC001756, which uses observations of wave speed to make local corrections to the bathymetry.